Exponent Rules Reference
Positive exponent: repeated multiplication (2^3 = 8). Zero exponent: any non-zero base^0 = 1. Negative exponent: 1/base^|n|. Fractional exponent: x^(p/q) = the q-th root of x, raised to the p-th power. Very large or small results are shown in scientific notation.
Frequently Asked Questions
An exponent tells you how many times to multiply a number by itself. For example, 2³ = 2 × 2 × 2 = 8. The number being multiplied is the base, and the superscript number is the exponent or power.
A negative exponent means the reciprocal: x⁻ⁿ = 1/xⁿ. For example, 2⁻³ = 1/2³ = 1/8 = 0.125. Negative exponents are commonly used in scientific notation for very small numbers (e.g., 10⁻⁶ = 0.000001 = one millionth).
A fractional exponent represents a root: x^(1/n) = the nth root of x. For example, 8^(1/3) = cube root of 8 = 2. Combined: 8^(2/3) = (cube root of 8)² = 4. This connects exponents and roots through the unified power rule.
Any non-zero number raised to the power of zero equals 1: x⁰ = 1. This follows from the exponent division rule: xⁿ / xⁿ = x⁰ = 1. The expression 0⁰ is mathematically undefined (or sometimes defined as 1 by convention).
The main rules are: xᵃ × xᵇ = xᵃ⁺ᵇ (multiply same base: add exponents). xᵃ / xᵇ = xᵃ⁻ᵇ (divide same base: subtract exponents). (xᵃ)ᵇ = xᵃᵇ (power of a power: multiply exponents). (xy)ⁿ = xⁿyⁿ (power of a product). x⁻ⁿ = 1/xⁿ (negative exponent).
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